001// Copyright (c) FIRST and other WPILib contributors. 002// Open Source Software; you can modify and/or share it under the terms of 003// the WPILib BSD license file in the root directory of this project. 004 005package edu.wpi.first.math.filter; 006 007import edu.wpi.first.math.MathSharedStore; 008import edu.wpi.first.math.MathUsageId; 009import edu.wpi.first.util.DoubleCircularBuffer; 010import java.util.Arrays; 011import org.ejml.simple.SimpleMatrix; 012 013/** 014 * This class implements a linear, digital filter. All types of FIR and IIR filters are supported. 015 * Static factory methods are provided to create commonly used types of filters. 016 * 017 * <p>Filters are of the form: y[n] = (b0 x[n] + b1 x[n-1] + ... + bP x[n-P]) - (a0 y[n-1] + a2 018 * y[n-2] + ... + aQ y[n-Q]) 019 * 020 * <p>Where: y[n] is the output at time "n" x[n] is the input at time "n" y[n-1] is the output from 021 * the LAST time step ("n-1") x[n-1] is the input from the LAST time step ("n-1") b0...bP are the 022 * "feedforward" (FIR) gains a0...aQ are the "feedback" (IIR) gains IMPORTANT! Note the "-" sign in 023 * front of the feedback term! This is a common convention in signal processing. 024 * 025 * <p>What can linear filters do? Basically, they can filter, or diminish, the effects of 026 * undesirable input frequencies. High frequencies, or rapid changes, can be indicative of sensor 027 * noise or be otherwise undesirable. A "low pass" filter smooths out the signal, reducing the 028 * impact of these high frequency components. Likewise, a "high pass" filter gets rid of slow-moving 029 * signal components, letting you detect large changes more easily. 030 * 031 * <p>Example FRC applications of filters: - Getting rid of noise from an analog sensor input (note: 032 * the roboRIO's FPGA can do this faster in hardware) - Smoothing out joystick input to prevent the 033 * wheels from slipping or the robot from tipping - Smoothing motor commands so that unnecessary 034 * strain isn't put on electrical or mechanical components - If you use clever gains, you can make a 035 * PID controller out of this class! 036 * 037 * <p>For more on filters, we highly recommend the following articles:<br> 038 * <a 039 * href="https://en.wikipedia.org/wiki/Linear_filter">https://en.wikipedia.org/wiki/Linear_filter</a> 040 * <br> 041 * <a href="https://en.wikipedia.org/wiki/Iir_filter">https://en.wikipedia.org/wiki/Iir_filter</a> 042 * <br> 043 * <a href="https://en.wikipedia.org/wiki/Fir_filter">https://en.wikipedia.org/wiki/Fir_filter</a> 044 * <br> 045 * 046 * <p>Note 1: calculate() should be called by the user on a known, regular period. You can use a 047 * Notifier for this or do it "inline" with code in a periodic function. 048 * 049 * <p>Note 2: For ALL filters, gains are necessarily a function of frequency. If you make a filter 050 * that works well for you at, say, 100Hz, you will most definitely need to adjust the gains if you 051 * then want to run it at 200Hz! Combining this with Note 1 - the impetus is on YOU as a developer 052 * to make sure calculate() gets called at the desired, constant frequency! 053 */ 054public class LinearFilter { 055 private final DoubleCircularBuffer m_inputs; 056 private final DoubleCircularBuffer m_outputs; 057 private final double[] m_inputGains; 058 private final double[] m_outputGains; 059 060 private static int instances; 061 062 /** 063 * Create a linear FIR or IIR filter. 064 * 065 * @param ffGains The "feedforward" or FIR gains. 066 * @param fbGains The "feedback" or IIR gains. 067 */ 068 public LinearFilter(double[] ffGains, double[] fbGains) { 069 m_inputs = new DoubleCircularBuffer(ffGains.length); 070 m_outputs = new DoubleCircularBuffer(fbGains.length); 071 m_inputGains = Arrays.copyOf(ffGains, ffGains.length); 072 m_outputGains = Arrays.copyOf(fbGains, fbGains.length); 073 074 instances++; 075 MathSharedStore.reportUsage(MathUsageId.kFilter_Linear, instances); 076 } 077 078 /** 079 * Creates a one-pole IIR low-pass filter of the form: y[n] = (1-gain) x[n] + gain y[n-1] where 080 * gain = e<sup>-dt / T</sup>, T is the time constant in seconds. 081 * 082 * <p>Note: T = 1 / (2 pi f) where f is the cutoff frequency in Hz, the frequency above which the 083 * input starts to attenuate. 084 * 085 * <p>This filter is stable for time constants greater than zero. 086 * 087 * @param timeConstant The discrete-time time constant in seconds. 088 * @param period The period in seconds between samples taken by the user. 089 * @return Linear filter. 090 */ 091 public static LinearFilter singlePoleIIR(double timeConstant, double period) { 092 double gain = Math.exp(-period / timeConstant); 093 double[] ffGains = {1.0 - gain}; 094 double[] fbGains = {-gain}; 095 096 return new LinearFilter(ffGains, fbGains); 097 } 098 099 /** 100 * Creates a first-order high-pass filter of the form: y[n] = gain x[n] + (-gain) x[n-1] + gain 101 * y[n-1] where gain = e<sup>-dt / T</sup>, T is the time constant in seconds. 102 * 103 * <p>Note: T = 1 / (2 pi f) where f is the cutoff frequency in Hz, the frequency below which the 104 * input starts to attenuate. 105 * 106 * <p>This filter is stable for time constants greater than zero. 107 * 108 * @param timeConstant The discrete-time time constant in seconds. 109 * @param period The period in seconds between samples taken by the user. 110 * @return Linear filter. 111 */ 112 public static LinearFilter highPass(double timeConstant, double period) { 113 double gain = Math.exp(-period / timeConstant); 114 double[] ffGains = {gain, -gain}; 115 double[] fbGains = {-gain}; 116 117 return new LinearFilter(ffGains, fbGains); 118 } 119 120 /** 121 * Creates a K-tap FIR moving average filter of the form: y[n] = 1/k (x[k] + x[k-1] + ... + x[0]). 122 * 123 * <p>This filter is always stable. 124 * 125 * @param taps The number of samples to average over. Higher = smoother but slower. 126 * @return Linear filter. 127 * @throws IllegalArgumentException if number of taps is less than 1. 128 */ 129 public static LinearFilter movingAverage(int taps) { 130 if (taps <= 0) { 131 throw new IllegalArgumentException("Number of taps was not at least 1"); 132 } 133 134 double[] ffGains = new double[taps]; 135 Arrays.fill(ffGains, 1.0 / taps); 136 137 double[] fbGains = new double[0]; 138 139 return new LinearFilter(ffGains, fbGains); 140 } 141 142 /** 143 * Creates a finite difference filter that computes the nth derivative of the input given the 144 * specified stencil points. 145 * 146 * <p>Stencil points are the indices of the samples to use in the finite difference. 0 is the 147 * current sample, -1 is the previous sample, -2 is the sample before that, etc. Don't use 148 * positive stencil points (samples from the future) if the LinearFilter will be used for 149 * stream-based online filtering (e.g., taking derivative of encoder samples in real-time). 150 * 151 * @param derivative The order of the derivative to compute. 152 * @param stencil List of stencil points. Its length is the number of samples to use to compute 153 * the given derivative. This must be one more than the order of the derivative or higher. 154 * @param period The period in seconds between samples taken by the user. 155 * @return Linear filter. 156 * @throws IllegalArgumentException if derivative < 1, samples <= 0, or derivative >= 157 * samples. 158 */ 159 public static LinearFilter finiteDifference(int derivative, int[] stencil, double period) { 160 // See 161 // https://en.wikipedia.org/wiki/Finite_difference_coefficient#Arbitrary_stencil_points 162 // 163 // For a given list of stencil points s of length n and the order of 164 // derivative d < n, the finite difference coefficients can be obtained by 165 // solving the following linear system for the vector a. 166 // 167 // [s₁⁰ ⋯ sₙ⁰ ][a₁] [ δ₀,d ] 168 // [ ⋮ ⋱ ⋮ ][⋮ ] = d! [ ⋮ ] 169 // [s₁ⁿ⁻¹ ⋯ sₙⁿ⁻¹][aₙ] [δₙ₋₁,d] 170 // 171 // where δᵢ,ⱼ are the Kronecker delta. The FIR gains are the elements of the 172 // vector 'a' in reverse order divided by hᵈ. 173 // 174 // The order of accuracy of the approximation is of the form O(hⁿ⁻ᵈ). 175 176 if (derivative < 1) { 177 throw new IllegalArgumentException( 178 "Order of derivative must be greater than or equal to one."); 179 } 180 181 int samples = stencil.length; 182 183 if (samples <= 0) { 184 throw new IllegalArgumentException("Number of samples must be greater than zero."); 185 } 186 187 if (derivative >= samples) { 188 throw new IllegalArgumentException( 189 "Order of derivative must be less than number of samples."); 190 } 191 192 var S = new SimpleMatrix(samples, samples); 193 for (int row = 0; row < samples; ++row) { 194 for (int col = 0; col < samples; ++col) { 195 S.set(row, col, Math.pow(stencil[col], row)); 196 } 197 } 198 199 // Fill in Kronecker deltas: https://en.wikipedia.org/wiki/Kronecker_delta 200 var d = new SimpleMatrix(samples, 1); 201 for (int i = 0; i < samples; ++i) { 202 d.set(i, 0, (i == derivative) ? factorial(derivative) : 0.0); 203 } 204 205 var a = S.solve(d).divide(Math.pow(period, derivative)); 206 207 // Reverse gains list 208 double[] ffGains = new double[samples]; 209 for (int i = 0; i < samples; ++i) { 210 ffGains[i] = a.get(samples - i - 1, 0); 211 } 212 213 return new LinearFilter(ffGains, new double[0]); 214 } 215 216 /** 217 * Creates a backward finite difference filter that computes the nth derivative of the input given 218 * the specified number of samples. 219 * 220 * <p>For example, a first derivative filter that uses two samples and a sample period of 20 ms 221 * would be 222 * 223 * <pre><code> 224 * LinearFilter.backwardFiniteDifference(1, 2, 0.02); 225 * </code></pre> 226 * 227 * @param derivative The order of the derivative to compute. 228 * @param samples The number of samples to use to compute the given derivative. This must be one 229 * more than the order of derivative or higher. 230 * @param period The period in seconds between samples taken by the user. 231 * @return Linear filter. 232 */ 233 public static LinearFilter backwardFiniteDifference(int derivative, int samples, double period) { 234 // Generate stencil points from -(samples - 1) to 0 235 int[] stencil = new int[samples]; 236 for (int i = 0; i < samples; ++i) { 237 stencil[i] = -(samples - 1) + i; 238 } 239 240 return finiteDifference(derivative, stencil, period); 241 } 242 243 /** Reset the filter state. */ 244 public void reset() { 245 m_inputs.clear(); 246 m_outputs.clear(); 247 } 248 249 /** 250 * Resets the filter state, initializing internal buffers to the provided values. 251 * 252 * <p>These are the expected lengths of the buffers, depending on what type of linear filter used: 253 * 254 * <table> 255 * <tr><th>Type</th><th>Input Buffer Length</th><th>Output Buffer Length</th></tr> 256 * <tr><td>Unspecified</td><td>length of {@code ffGains}</td><td>length of {@code fbGains}</td> 257 * </tr> 258 * <tr><td>Single Pole IIR</td><td>1</td><td>1</td></tr> 259 * <tr><td>High-Pass</td><td>2</td><td>1</td></tr> 260 * <tr><td>Moving Average</td><td>{@code taps}</td><td>0</td></tr> 261 * <tr><td>Finite Difference</td><td>length of {@code stencil}</td><td>0</td></tr> 262 * <tr><td>Backward Finite Difference</td><td>{@code samples}</td><td>0</td></tr> 263 * </table> 264 * 265 * @param inputBuffer Values to initialize input buffer. 266 * @param outputBuffer Values to initialize output buffer. 267 * @throws IllegalArgumentException if length of inputBuffer or outputBuffer does not match the 268 * length of ffGains and fbGains provided in the constructor. 269 */ 270 public void reset(double[] inputBuffer, double[] outputBuffer) { 271 // Clear buffers 272 reset(); 273 274 if (inputBuffer.length != m_inputGains.length || outputBuffer.length != m_outputGains.length) { 275 throw new IllegalArgumentException("Incorrect length of inputBuffer or outputBuffer"); 276 } 277 278 for (double input : inputBuffer) { 279 m_inputs.addFirst(input); 280 } 281 for (double output : outputBuffer) { 282 m_outputs.addFirst(output); 283 } 284 } 285 286 /** 287 * Calculates the next value of the filter. 288 * 289 * @param input Current input value. 290 * @return The filtered value at this step 291 */ 292 public double calculate(double input) { 293 double retVal = 0.0; 294 295 // Rotate the inputs 296 if (m_inputGains.length > 0) { 297 m_inputs.addFirst(input); 298 } 299 300 // Calculate the new value 301 for (int i = 0; i < m_inputGains.length; i++) { 302 retVal += m_inputs.get(i) * m_inputGains[i]; 303 } 304 for (int i = 0; i < m_outputGains.length; i++) { 305 retVal -= m_outputs.get(i) * m_outputGains[i]; 306 } 307 308 // Rotate the outputs 309 if (m_outputGains.length > 0) { 310 m_outputs.addFirst(retVal); 311 } 312 313 return retVal; 314 } 315 316 /** 317 * Returns the last value calculated by the LinearFilter. 318 * 319 * @return The last value. 320 */ 321 public double lastValue() { 322 return m_outputs.getFirst(); 323 } 324 325 /** 326 * Factorial of n. 327 * 328 * @param n Argument of which to take factorial. 329 */ 330 private static int factorial(int n) { 331 if (n < 2) { 332 return 1; 333 } else { 334 return n * factorial(n - 1); 335 } 336 } 337}